Contributions. In this paper, we focus on blind demixing of graph signals.
In particular, the observed graph signal \(\mathbf {y}\)  is assumed to be the combination (sum) of the diffused graph signals \(\lbrace \mathbf {y}_\text{i}\rbrace _{\text{i}=1}^\text{R}\) , each of which is modeled as the output of a graph filter with coefficients \(\mathbf {h}_\text{i}\)  excited with an input graph signal \(\mathbf {x}_\text{i}\) .
The signal \(\mathbf {x}_\text{i}\)  is assumed to be localized in a subset of the nodes of the \(\text{i}\) th graph. In this setting we seek to demix the observed signal \(\mathbf {y}\)  by jointly estimating the input graph signals as well as the filters coefficients. This extends the classical problem of blind source separation or demixing of signals in the time and spatial domains. Apart from its theoretical interest, identification of diffused graph signals also bears practical relevance, since they have been shown to be germane to, e.g., explaining the structure of real-world datasets [1]}, [2]} as well as understanding the dynamics of linear network diffusion processes [3]}, [2]}, [5]}.
